Abstract
We study the rate of convergence in periodic homogenization for convex Hamilton–Jacobi equations with multiscales, where the Hamiltonian depends on both of the spatial variable and the oscillatory variable. In particular, we show that for the Cauchy problem, the rate of convergence is by optimal control formulas, scale separations and curve cutting techniques. We also show the rate of homogenization for the static problem based on the same idea. Additionally, we provide examples that illustrate the rate of convergence for the Cauchy problem is optimal for and .
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